非平衡系におけるリズミックな時空間パターンのダイナミクスと制御

• Project Area: Synergy of Fluctuation and Structure:Foundation of Universal Laws in Nonequilibrium Systems
• Project/Area Number: 26103510
• Research Category: Grant-in-Aid for Scientific Research on Innovative Areas (Research in a proposed research area)
• Allocation Type: Single-year Grants
• Review Section: Science and Engineering
• Research Institution: Tokyo Institute of Technology
• Principal Investigator: 中尾 裕也 東京工業大学, 大学院情報理工学研究科, 准教授 (40344048)
• Project Period (FY): 2014-04-01 – 2016-03-31
• Project Status: Completed (Fiscal Year 2015)
• Budget Amount: ¥3,380,000 (Direct Cost: ¥2,600,000、Indirect Cost: ¥780,000); Fiscal Year 2015: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000); Fiscal Year 2014: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000)
• Keywords: 非線形ダイナミクス / 同期現象 / 縮約理論 / 非線形振動 / カルマン渦列 / 時空間パターン / リズム現象 / 自己組織化

Outline of Annual Research Achievements

昨年度までの研究で、従来の低次元力学系の非線形振動現象に対する位相縮約理論を、無限次元の力学系である反応拡散系のリズミックな時空間パターンや、Hele-Shawセル中の流体の振動的熱対流に対して拡張できることを示し、それらの系の同期現象などを議論した。今年度の研究では、それらの研究をさらに発展させ、より複雑な流れ場の非線形振動の解析を目的として、格子ボルツマン法によって記述される流れ場の非線形振動に対する位相縮約法を発展させた。特に、流体系の典型的な非線形振動現象として、流れ場中に置いた障害物によって生じる周期的なカルマン渦列を対象とし、その摂動に対する位相感受関数を求めて位相方程式を導出し、これを用いて周期的な外力による流れ場の同期現象を解析した。格子ボルツマン法のアルゴリズムが決定論的な力学系と見なせるという性質を利用して、周期的なカルマン渦列に対応するリミットサイクル振動状態にある格子ボルツマン系に対して、その位相感受関数を与える随伴方程式を導出し、これを数値的に解くことによって位相感受関数を求めた。ここで、位相感受関数は流れ場（正確には流れ場を構成する粒子の速度分布）に与えた微小摂動が系の非線形振動の長時間後の位相にどのような変化を及ぼすかを定量化するもので、位相縮約理論における本質的な量である。数値計算により系の流れ場に摂動を与えて直接測定した位相応答関数との比較も行い、随伴方程式から得た位相感受関数の妥当性を確認した。これにより、弱摂動を受ける周期的なカルマン渦列を1次元の位相方程式で記述できる、すなわち位相縮約できることが示された。この理論の応用例として、周期外力によるカルマン渦列の同期現象を解析し、理論的な結果と直接数値シミュレーションの結果がよく一致することを確認した。

Research Progress Status

27年度が最終年度であるため、記入しない。

Strategy for Future Research Activity

27年度が最終年度であるため、記入しない。

Research Products

• [Journal Article] Phase reduction approach to synchronization of nonlinear oscillators (2016)
  • Author(s): Hiroya Nakao
  • Journal Title: Contemporary Physics Volume: 57 Issue: 2 Pages: 188-214
  • DOI: 10.1080/00107514.2015.1094987
  • Peer Reviewed / Acknowledgement Compliant
• [Journal Article] A criterion for timescale decomposition of external inputs for generalized phase reduction of limit-cycle oscillators (2015)
  • Author(s): Wataru Kurebayashi, Sho Shirasaka, and Hiroya Nakao
  • Journal Title: Nonlinear Theory and Its Applications, IEICE Volume: 6 Issue: 2 Pages: 171-180
  • DOI: 10.1587/nolta.6.171
  • NAID: 130005064241
  • ISSN: 2185-4106
  • Peer Reviewed / Open Access / Acknowledgement Compliant
• [Journal Article] Phase description of oscillatory convection with a spatially translational mode (2015)
  • Author(s): Yoji Kawamura and Hiroya Nakao
  • Journal Title: Physica D Volume: 295-296 Pages: 11-29
  • DOI: 10.1016/j.physd.2014.12.007
  • Peer Reviewed / Open Access / Acknowledgement Compliant
• [Journal Article] Design and control of noise-induced synchronization patterns (2014)
  • Author(s): W. Kurebayashi, T. Ishiil, M. Hasegawa and H. Nakao
  • Journal Title: Europhysics Letters Volume: 107 Issue: 1 Pages: 10009-10009
  • DOI: 10.1209/0295-5075/107/10009
  • Peer Reviewed / Open Access
• [Journal Article] Complex Ginzburg-Landau equation on networks and its non-uniform dynamics (2014)
  • Author(s): Hiroya Nakao
  • Journal Title: European Physical Journal Special Topics Volume: 223 Issue: 12 Pages: 2411-2421
  • DOI: 10.1140/epjst/e2014-02220-1
  • Peer Reviewed / Acknowledgement Compliant
• [Journal Article] Phase reduction approach to synchronization of spatiotemporal rhythms in reaction-diffusion systems (2014)
  • Author(s): Hiroya Nakao, Tatsuo Yanagita, and Yoji Kawamura
  • Journal Title: Physical Review X Volume: 4 Issue: 2 Pages: 021032-021055
  • DOI: 10.1103/physrevx.4.021032
  • NAID: 120006582330
  • Peer Reviewed / Open Access
• [Presentation] Stability and sensitivity of synchronized states in a network of symmetrically coupled nonlinear oscillators for generating gait patterns (2015)
  • Author(s): Masashi Ota, Sho Yasui, Sho Shirasaka, and Hiroya Nakao
  • Organizer: NOLTA2015
  • Place of Presentation: Hong Kong, China
  • Year and Date: 2015-12-01
  • Int'l Joint Research
• [Presentation] Uncontrolled manifold analysis of oscillatory motions in dynamical models of body movement based on the Floquet theory (2015)
  • Author(s): Sho Shirasaka, Wataru Kurebayashi, and Hiroya Nakao
  • Organizer: NOLTA2015
  • Place of Presentation: Hong Kong, China
  • Year and Date: 2015-12-01
  • Int'l Joint Research
• [Presentation] Phase description of Karman vortices (2015)
  • Author(s): Yosuke Tomaru, Sho Shirasaka, Wataru Kurebayashi, and Hiroya Nakao
  • Organizer: International Symposium on Fluctuation and Structure out of Equilibrium 2015
  • Place of Presentation: Kyoto, Japan
  • Year and Date: 2015-08-20
  • Int'l Joint Research
• [Presentation] Phase reduction analysis of rhythmic spatiotemporal patterns and network dynamics (2015)
  • Author(s): Hiroya Nakao
  • Organizer: Dynamics of Coupled Oscillators: 40 years of the Kuramoto Model
  • Place of Presentation: Dresden, Germany
  • Year and Date: 2015-07-27
  • Int'l Joint Research / Invited
• [Presentation] Synchronization of rhythmic spatiotemporal patterns and network dynamics (2015)
  • Author(s): Hiroya Nakao
  • Organizer: 8th International Conference Engineering of Chemical Complexity
  • Place of Presentation: Munich, Germany
  • Year and Date: 2015-06-22
  • Int'l Joint Research / Invited
• [Presentation] Phase Reduction Approach to Synchronization of Coupled Oscillator Networks (2015)
  • Author(s): Hiroya Nakao
  • Organizer: International Symposium on Photonics and Electronics Science and Engineering 2015
  • Place of Presentation: Katsura-Hall, Katsura-Campus, Kyoto University, Kyoto, Japan
  • Year and Date: 2015-03-09
  • Invited
• [Presentation] Synchronization Analysis of Oscillator Circuits by Quadratic Phase Models (2014)
  • Author(s): Wataru Kurebayashi, Sho Shirasaka, and Hiroya Nakao
  • Organizer: 3rd Japan-Korea Joint Workshop on Complex Communication Sciences
  • Place of Presentation: Paradise Hotel, Busan, Korea
  • Year and Date: 2014-10-27 – 2014-10-28
• [Presentation] Bayesian Parameter Estimation of Non-Stationary Collective Dynamics in Moving Animal Groups (2014)
  • Author(s): Ken Nishikawa, Wataru Kurebayashi, Hiroya Nakao
  • Organizer: 2014 International Symposium on Nonlinear Theory and its Applications
  • Place of Presentation: Luzern, Switzerland
  • Year and Date: 2014-09-14 – 2014-09-18
• [Presentation] Robust synchronization analysis by quadratic phase equation (2014)
  • Author(s): Wataru Kurebayashi, Sho Shirasaka, and Hiroya Nakao
  • Organizer: XXXIV Dynamics Days Europe
  • Place of Presentation: University of Bayreuth, Germany
  • Year and Date: 2014-09-08 – 2014-09-12
• [Presentation] Optimal entrainment of rhythmic patterns in reaction-diffusion systems by periodic spatiotemporal forcing (2014)
  • Author(s): Hiroya Nakao, Tatsuo Yanagita, and Yoji Kawamura
  • Organizer: Gordon Research Conference: Oscillations & Dynamic Instabilities in Chemical Systems
  • Place of Presentation: Melia Golf Vichy Catalan Business and Convention Center, Girona, Spain
  • Year and Date: 2014-07-13 – 2014-07-18
• [Remarks] Hiroya Nakao papers
  • URL: http://www.k.mei.titech.ac.jp/members/nakao/papers.html
• [Remarks] Hiroya Nakao Papers
  • URL: http://www.k.mei.titech.ac.jp/members/nakao/papers.html